Let's learn how to use definite Integration to find areas under curves in A-Level Maths!

**Definite integral and area**

To find the area under a curve, between two values of x, you follow the process of definite integrals.

The values of a and b will be the limits of the Area, and y is the function of the curve.

Itis important to note that when we say ‘__the area under the curve__’, this means the area __between the curve and the x-axis__.

**Example Question**

Find the value of R, where R is the area between the values of x = 1 and x = 3, and under the following curve:

y= x^{2} + 4/x^{2}

**Area under the x-axis**

Find the area of the finite region bounded by the curve y = x(x – 3) and the x-axis

1. Start with a sketch…

2. The graph will cross the x-axis at 0 and 3…

So the area is 4.5 square units (you can write is as a positive value…)

**Area both above and below x-axis **

Find the area between the curve:

y= x(x + 1)(x – 1) and the x-axis

You need to integrate each section separately and then combine them (as positive values…)

The total area is therefore 1 square unit.

Drafted by Eunice (Maths)

Reference

https://www.mathsisfun.com/calculus/integration-definite.html